What does he mean when he says he "accused his brother of acting like an heir, unable to understand why his younger brother was not content to be a spare"? What is his obsession with being a "spare"? It's a simple fact of life that he was born second and was therefore second in line to the throne, it wasn't William's fault and he couldn't change it. It would also not be unnatural for William to have in mind his future responsibilities when talking to his brother.
He seems to be obsessed with this "spare" issue and maybe that is what is at the root of all his actions. If he had any sense, he would thank God that he's not landed with having to be King and all the shit that goes with that, and just get on with his life.